A Novel Method for Generating Benchmark Functions Using Recurrent Neural Network

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10361)


In recent years numerous evolutionary algorithms have been proposed to optimize multi–modal problems. These algorithms test the performance by benchmark functions for simulating real-world problems. However, the benchmark functions don’t have enough similarity and complexity compared to real world. Thus, Recurrent Benchmark Generator (RBG) is proposed in this paper to generate complex and different benchmark functions. This generator obtains a mass of modals by recurrent neural network, which are added various fluctuations of normal benchmark functions to keep a balance between complexity and gradient. The experimental results indicate that the novel approach produces more complex benchmark functions which are more conformed to real world problems.


Benchmark function Recurrent neural network Random Probability density 



This work was supported by National Natural Science Foundation of China under Grant No. 61572230, No. 61573166, No. 61373054, No. 61472164, No. 61472163, No. 61672262, No. 61640218, Shandong Provincial Natural Science Foundation, China, under Grant ZR2015JL025, ZR2014JL042. Science and technology project of Shandong Province under Grant No. 2015GGX101025, Project of Shandong Province Higher Educational Science and Technology Program under Grant no. J16LN07. Shandong Provincial Key R&D Program under Grant No. 2016ZDJS01A12, No. 2016GGX101001.


  1. 1.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
  2. 2.
    Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39–43. IEEE (1995)Google Scholar
  3. 3.
    Wang, L., Yang, B., Orchard, J.: Particle swarm optimization using dynamic tournament topology. Appl. Soft Comput. 48, 584–596 (2016)CrossRefGoogle Scholar
  4. 4.
    Wang, L., Yang, B., Abraham, A.: Distilling middle-age cement hydration kinetics from observed data using phased hybrid evolution. Soft. Comput. 20(9), 3637–3656 (2016)CrossRefGoogle Scholar
  5. 5.
    Wang, L., Yang, B., Chen, Y., Zhang, X., Orchard, J.: Improving neural-network classifiers using nearest neighbor partitioning. IEEE Trans. Neural Netw. Learn. Syst. (2016, in Press). doi:10.1109/TNNLS.2016.2580570
  6. 6.
    Qu, B.Y., Liang, J.J., Wang, Z.Y., Chen, Q., Suganthan, P.N.: Novel benchmark functions for continuous multimodal optimization with comparative results. Swarm Evol. Comput. 26, 23–34 (2016)CrossRefGoogle Scholar
  7. 7.
    Suganthan, P.N., Hansen, N., Liang, J.J., Deb, K., Chen, Y.P., Auger, A., Tiwari, S.: Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. KanGAL report, 2005005 (2005)Google Scholar
  8. 8.
    Li, T., Rogovchenko, Y.V.: Oscillation criteria for even-order neutral differential equations. Appl. Math. Lett. 61, 35–41 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Li, T., Rogovchenko, Y.V.: Oscillation of second-order neutral differential equations. Math. Nachr. 288(10), 1150–1162 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Mirjalili, S., Lewis, A.: Obstacles and difficulties for robust benchmark problems: a novel penalty-based robust optimisation method. Inf. Sci. 328, 485–509 (2016)CrossRefGoogle Scholar
  11. 11.
    Pineda, F.J.: Generalization of back-propagation to recurrent neural networks. Phys. Rev. Lett. 59(19), 2229 (1987)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Shandong Provincial Key Laboratory of Network Based Intelligent ComputingUniversity of JinanJinanChina

Personalised recommendations